Discussion on new properties of staircase waveform through connection to an infinite series

The staircase waveform produced by digital-to-analogue conversion is applied widely in electricity metrology, based on the known properties. However, a continuous investigation of new properties is still very important for its further applications. An infinite series is presented through analysis of the producing process of the staircase waveform. Based on the model of `digital-to-analogue converter (DAC) aliasing effect´, when the parameters of the series are extended from an integral to a real number, new properties are discussed. The concepts of `asynchronous sampling´, `sub-´ and `inter-harmonic´ and `under-Nyquist sampling´ are derived into DAC. The more interesting phenomena are detailed. The results of simulations and experiments are reported.